Session C4: Computational Physics I

SCAN: An Efficient Density Functional Yielding Accurate Structures and Energies of Diversely-Bonded Materials

The accuracy and computational efficiency of the widely used Kohn-Sham density functional theory (DFT) are limited by the approximation to its exchange-correlation energy E$_{xc}$. The earliest local density approximation (LDA) overestimates the strengths of all bonds near equilibrium (even the vdW bonds). By adding the electron density gradient to model E$_{xc}$, generalized gradient approximations (GGAs) generally soften the bonds to give robust and overall more accurate descriptions, except for the vdW interaction which is largely lost. Further improvement for covalent, ionic, and hydrogen bonds can be obtained by the computationally more expensive hybrid GGAs, which mix GGAs with the nonlocal exact exchange. Meta-GGAs are still semilocal in computation and thus efficient. Compared to GGAs, they add the kinetic energy density that enables them to recognize and accordingly treat different bonds, which no LDA or GGA can [1]. We show here that the recently developed non-empirical strongly constrained and appropriately normed (SCAN) meta-GGA [2] improves significantly over LDA and the standard Perdew-Burke-Ernzerhof GGA for geometries and energies of diversely-bonded materials (including covalent, metallic, ionic, hydrogen, and vdW bonds) at comparable efficiency [3]. Often SCAN matches or improves upon the accuracy of a hybrid functional, at almost-GGA cost. [1] J. Sun et al., Phys. Rev. Lett. 111, 106401 (2013). [2] J. Sun et al, Phys. Rev. Lett. 115, 036402 (2015). [3] J. Sun et al., Nat. Chem. \textbf{8}, 831 (2016).   

Structural and Ferroelectric Properties of Prototypical Ferroelectric Materials: Comparative first-principles investigations

Ferroelectricity originates from the breaking of spatial inversion symmetry, and spontaneous polarization is determined by the amplitude of the polar structural distortion. Although the density functional theory has been widely used for studying ferroelectric properties, an accurate quantitative prediction of the distortion is rather challenging and is to a great extent limited by the reliability of the adopted exchange-correlation functionals. For the most studied perovskites, the local density approximation (LDA) seems to be more reliable than the generalized gradient approximation (GGA). However, the cell volumes are usually strongly underestimated by the LDA. The B1-WC hybrid functional systematically improves the calculated ferroelectric properties, but its application is restricted to small systems because of the expensive computational effort. The recently developed strongly constrained and appropriately normed (SCAN) meta-GGA is accurate for geometries and energies of diversely-bonded materials. Here, we show that the SCAN is a universally accurate approach for predicting the structural and electric properties of several prototypical ferroelectric materials. The SCAN is comparable or more accurate than the B1-WC hybrid functional but with much cheaper computational cost.   

Density functional study on a light-harvesting carotenoid-porphyrin-C60 molecular triad in explicit solvent

We investigate the effect of solvent on the electronic structure of abiomimetic molecular triad that shows photoinduced charge transfer in laboratory. The supramolecular triad contains three different units -- C60, porphyrin, and beta-carotenoid. We have performed classical molecular dynamics simulation of the triad surrounded by 15000 water molecules using NAMD for 20 nanoseconds. Subsequently, we performed an all-electron density functional calculations (DFT) using large basis sets on the 50 snap-shots taken from the molecular dynamics simulation. The solvent effects in the DFT calculations are treated using both the explicit water molecules as well as using the point charge representation of water. The excitation energies and absorption spectra show that the polar solvent induces significant changes in the electronic structure of the triad.   

Invariant Representations of Materials (Or, Making Machine Learning Work)

Efforts to leverage computational materials science to impact meaningful materials discovery are driving rapid growth in materials data. Direct searching of computational databases has already yielded some discoveries. But to really capitalize on the investment and to utilize the full potential of the data, one must be able to effectively explore composition and structure space, a vastly larger space than the space of the data. In other words, we must find a way to effectively interpolate (in composition and structure space) between data points. Recently it has been understood that details of the mathematical representation of materials are key to developing effective algorithms. In simple terms, we discuss the features that a representation must have to be useful for standard data science approaches to be effective.   

Discovering materials using machine learning

Material scientists have developed huge experimental databases of known materials over the last century. Here at BYU we have built a large database of alloy simulations. The challenge now is to develop data$-$driven methods for designing and discovering new materials. Using such data driven paradigms and extracting the relevant information necessary from the data in a systematic way can be accomplished through an approach known as ``machine learning". Machine learning is a subfield of artificial intelligence pertaining to the creation of models that can effectively interpolate from a few known data points. In this talk, I will present a simple understanding of a machine learning model called ``scattering transforms" and its usage in discovering new materials. The scattering transform model gives a computer the ability to learn about materials with several elements without being programmed explicitly. This model offers the potential of high accuracy at the speed of machine learning thus accelerating materials discovery.   

Characterizing and Understanding Parameterized Models through Information Topology

Information Topology can be used to characterize and reduce complex models. Varying the parameters of a model through all possible values gives a manifold of possible predictions. The boundaries of the manifold correspond to reduced-parameter models, and are a topological feature. Our past work has focused on the cluster expansion often used in statistical mechanics. We have now developed a method suited to a much wider class of models. Analyzing this class of models has led to definition of new properties characterizing posets for which a minimal amount of information is sufficient to construct the entire manifold topology. We have characterized this class of models and identified several existing models that fall within it. Further, we have designed and implemented an algorithm for reconstructing the manifold topology from said minimal information. Characterizing the manifold topology of a complex model allows us to recognize relationships among behaviors of the model and simplified models.